diff --git a/Convex_hull_2/doc_tex/Convex_hull_2/convex_hull_2.tex b/Convex_hull_2/doc_tex/Convex_hull_2/convex_hull_2.tex index 25e617b48b5..a5a8524919d 100644 --- a/Convex_hull_2/doc_tex/Convex_hull_2/convex_hull_2.tex +++ b/Convex_hull_2/doc_tex/Convex_hull_2/convex_hull_2.tex @@ -60,7 +60,7 @@ simple polygonal chains (or polygons) is available through the function In the following example a convex hull is constructed from point data read from standard input using \ccc{Graham_Andrew} algorithm. The resulting convex -polygon is shown at the standard ouput console. The same results could be +polygon is shown at the standard output console. The same results could be achieved by substituting the function \ccc{CGAL::ch_graham_andrew} by other function like \ccc{CGAL::ch_bykat}. diff --git a/Convex_hull_2/doc_tex/Convex_hull_2/traits_classes_2.tex b/Convex_hull_2/doc_tex/Convex_hull_2/traits_classes_2.tex index 6cf5e84bb8e..9dd30fcdabc 100644 --- a/Convex_hull_2/doc_tex/Convex_hull_2/traits_classes_2.tex +++ b/Convex_hull_2/doc_tex/Convex_hull_2/traits_classes_2.tex @@ -1,7 +1,7 @@ \section{Traits Classes} Each of the functions used to compute convex hulls or extreme points -is paramterized by a traits class, which specifies the types and geometric +is parameterized by a traits class, which specifies the types and geometric primitives to be used in the computation. There are several implementations of 2D traits classes provided in the library. The class \ccc{Convex_hull_traits_2}\ccIndexMainItem[C]{Convex_hull_traits_2} diff --git a/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_akl_toussaint.tex b/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_akl_toussaint.tex index e70ff959719..22d24a895b9 100644 --- a/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_akl_toussaint.tex +++ b/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_akl_toussaint.tex @@ -44,7 +44,7 @@ type \ccc{ForwardIterator::value_type} is defined. \ccc{OutputIterator::value_type} are equivalent to \ccc{Traits::Point_2}. \item \ccc{Traits} defines the following subset of types from - the concept ConvexHullTraits\_2 and their corresponding member + the concept \ccc{ConvexHullTraits_2} and their corresponding member %\ccIndexMainItem[c]{ConvexHullTraits_2} functions that return instances of these types: \begin{itemize} diff --git a/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_bykat.tex b/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_bykat.tex index bcfddbeefd5..2faef5a130c 100644 --- a/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_bykat.tex +++ b/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_bykat.tex @@ -45,7 +45,7 @@ type \ccc{ForwardIterator::value_type} is defined. \ccc{OutputIterator::value_type} are equivalent to \ccc{Traits::Point_2}. \item \ccc{Traits} defines the following subset of types from - the concept ConvexHullTraits\_2 and their corresponding member + the concept \ccc{ConvexHullTraits_2} and their corresponding member %\ccIndexMainItem[c]{ConvexHullTraits_2} functions that return instances of these types: \begin{itemize} @@ -67,7 +67,7 @@ type \ccc{ForwardIterator::value_type} is defined. \ccRefIdfierPage{CGAL::convex_hull_2} \ccImplementation -This function implements the non-recursive varitaion of +This function implements the non-recursive variation of Eddy's algorithm \cite{e-nchap-77} described in \cite{b-chfsp-78}. This algorithm requires $O(n h)$ time in the worst case for $n$ input points with $h$ extreme points. diff --git a/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_e_point.tex b/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_e_point.tex index 482a7d2db3e..623ec907079 100644 --- a/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_e_point.tex +++ b/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_e_point.tex @@ -32,7 +32,7 @@ type \ccc{ForwardIterator::value_type} is defined. \ccHeading{Requirements} \ccc{Traits} defines a type \ccc{Traits::Less_xy_2} as described in -the concept ConvexHullTraits\_2 and the corresponding member +the concept \ccc{ConvexHullTraits_2} and the corresponding member %\ccIndexMainItem[c]{ConvexHullTraits_2} function that returns an instance of this type. diff --git a/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_eddy.tex b/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_eddy.tex index 13bb7745b15..5099890da2a 100644 --- a/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_eddy.tex +++ b/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_eddy.tex @@ -45,7 +45,7 @@ type \ccc{ForwardIterator::value_type} is defined. \ccc{OutputIterator::value_type} are equivalent to \ccc{Traits::Point_2}. \item \ccc{Traits} defines the following subset of types from - the concept ConvexHullTraits\_2 and their corresponding member + the concept \ccc{ConvexHullTraits_2} and their corresponding member %\ccIndexMainItem[c]{ConvexHullTraits_2} functions that return instances of these types: \begin{itemize} diff --git a/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_graham_andrew.tex b/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_graham_andrew.tex index 38b2f1467bb..f79e1e37f29 100644 --- a/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_graham_andrew.tex +++ b/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_graham_andrew.tex @@ -44,7 +44,7 @@ type \ccc{InputIterator::value_type} is defined. \ccc{OutputIterator::value_type} are equivalent to \ccc{Traits::Point_2}. \item \ccc{Traits} defines the following subset of types from - the concept ConvexHullTraits\_2 and their corresponding member + the concept \ccc{ConvexHullTraits_2} and their corresponding member %\ccIndexMainItem[c]{ConvexHullTraits_2} functions that return instances of these types: \begin{itemize} @@ -69,7 +69,7 @@ type \ccc{InputIterator::value_type} is defined. \ccImplementation This function implements Andrew's variant of the Graham -scan algorithm \cite{a-aeach-79} and follows the presenation of Mehlhorn +scan algorithm \cite{a-aeach-79} and follows the presentation of Mehlhorn \cite{m-mdscg-84}. This algorithm requires $O(n \log n)$ time in the worst case for $n$ input points. diff --git a/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_graham_andrew_scan.tex b/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_graham_andrew_scan.tex index 77defe9110c..207e1e2ded8 100644 --- a/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_graham_andrew_scan.tex +++ b/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_graham_andrew_scan.tex @@ -50,7 +50,7 @@ type \ccc{BidirectionalIterator::value_type} is defined. \ccc{OutputIterator::value_type} are equivalent to \ccc{Traits::Point_2}. \item \ccc{Traits} defines the following two types from - the concept ConvexHullTraits\_2 and their corresponding member + the concept \ccc{ConvexHullTraits_2} and their corresponding member %\ccIndexMainItem[c]{ConvexHullTraits_2} functions that return instances of these types: \begin{itemize} @@ -78,7 +78,7 @@ In the following example \ccc{ch_graham_andrew_scan()} is used to realize Anderson's variant \cite{a-readc-78} of the Graham Scan \cite{g-eadch-72}. The points are sorted counterclockwise around the leftmost point using the \ccc{Less_rotate_ccw_2} predicate, as defined in -the concept ConvexHullTraits\_2. According to the definition +the concept \ccc{ConvexHullTraits_2}. According to the definition of \ccc{Less_rotate_ccw_2}, the leftmost point is the last point in the sorted sequence and its predecessor on the convex hull is the first point in the sorted sequence. It is not hard to see that the preconditions of diff --git a/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_jarvis.tex b/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_jarvis.tex index bc8f27b7926..24179345b39 100644 --- a/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_jarvis.tex +++ b/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_jarvis.tex @@ -45,7 +45,7 @@ type \ccc{InputIterator::value_type} is defined. \ccc{OutputIterator::value_type} are equivalent to \ccc{Traits::Point_2}. \item \ccc{Traits} defines the following subset of types from - the concept ConvexHullTraits\_2 and their corresponding member + the concept \ccc{ConvexHullTraits_2} and their corresponding member %\ccIndexMainItem[c]{ConvexHullTraits_2} functions that return instances of these types: \begin{itemize} diff --git a/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_jarvis_march.tex b/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_jarvis_march.tex index 6a487338b09..5abecddf257 100644 --- a/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_jarvis_march.tex +++ b/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_jarvis_march.tex @@ -48,7 +48,7 @@ type \ccc{ForwardIterator::value_type} is defined. \ccc{OutputIterator::value_type} are equivalent to \ccc{Traits::Point_2}. \item \ccc{Traits} defines the following subset of types from - the concept ConvexHullTraits\_2 and their corresponding member + the concept \ccc{ConvexHullTraits_2} and their corresponding member %\ccIndexMainItem[c]{ConvexHullTraits_2} functions that return instances of these types: \begin{itemize} diff --git a/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_melkman.tex b/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_melkman.tex index 6cfd6edfaca..b81be91a4bd 100644 --- a/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_melkman.tex +++ b/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_melkman.tex @@ -42,7 +42,7 @@ type \ccc{InputIterator::value_type} is defined. \item \ccc{InputIterator::value_type} and \ccc{OutputIterator::value_type} are equivalent to \ccc{Traits::Point_2}. \item \ccc{Traits} contains the following subset of types from - the concept ConvexHullTraits\_2 and their corresponding member + the concept \ccc{ConvexHullTraits_2} and their corresponding member %\ccIndexMainItem[c]{ConvexHullTraits_2} functions that return instances of these types: \begin{itemize} diff --git a/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_n_point.tex b/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_n_point.tex index 86d5cac36fe..c32bdccee1d 100644 --- a/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_n_point.tex +++ b/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_n_point.tex @@ -33,7 +33,7 @@ The default traits class \ccc{Default_traits} is the kernel in which the type \ccHeading{Requirements} \ccc{Traits} defines the type \ccc{Traits::Less_yx_2} as specified in -the concept ConvexHullTraits\_2 and the corresponding member +the concept \ccc{ConvexHullTraits_2} and the corresponding member function that returns an instance of this type. diff --git a/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_ns_point.tex b/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_ns_point.tex index 4a714adcac2..1d21da98aca 100644 --- a/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_ns_point.tex +++ b/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_ns_point.tex @@ -36,7 +36,7 @@ type \ccc{ForwardIterator::value_type} is defined. \ccHeading{Requirements} \ccc{Traits} defines the type \ccc{Traits::Less_yx_2} as specified in -the concept ConvexHullTraits\_2 and the corresponding member +the concept \ccc{ConvexHullTraits_2} and the corresponding member function that returns an instance of this type. diff --git a/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_nswe_point.tex b/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_nswe_point.tex index 9aed5fc0939..0fcc645aacd 100644 --- a/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_nswe_point.tex +++ b/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_nswe_point.tex @@ -39,7 +39,7 @@ minimal $x$, and maximal $x$ coordinates. \ccHeading{Requirements} \ccc{Traits} contains the following subset of types from -the concept ConvexHullTraits\_2 and their corresponding member +the concept \ccc{ConvexHullTraits_2} and their corresponding member functions that return instances of these types: \begin{itemize} \item \ccc{Traits::Less_xy_2}, diff --git a/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_s_point.tex b/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_s_point.tex index 81412c8f7f7..bfcea0de87f 100644 --- a/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_s_point.tex +++ b/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_s_point.tex @@ -33,7 +33,7 @@ type \ccc{ForwardIterator::value_type} is defined. \ccHeading{Requirements} \ccc{Traits} defines the type \ccc{Traits::Less_yx_2} as specified in -the concept ConvexHullTraits\_2 and the corresponding member +the concept \ccc{ConvexHullTraits_2} and the corresponding member function that returns an instance of this type. diff --git a/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_w_point.tex b/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_w_point.tex index 22325a1d10d..468d8566799 100644 --- a/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_w_point.tex +++ b/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_w_point.tex @@ -30,7 +30,7 @@ of input points with minimal $x$ coordinate. \ccHeading{Requirements} \ccc{Traits} defines the type \ccc{Traits::Less_xy_2} as specified in -the concept ConvexHullTraits\_2 and the corresponding member +the concept \ccc{ConvexHullTraits_2} and the corresponding member function that returns an instance of this type. diff --git a/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_we_point.tex b/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_we_point.tex index bfc8fede1fe..47ca33e1e58 100644 --- a/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_we_point.tex +++ b/Convex_hull_2/doc_tex/Convex_hull_2_ref/ch_we_point.tex @@ -36,7 +36,7 @@ type \ccc{ForwardIterator::value_type} is defined. \ccHeading{Requirements} \ccc{Traits} defines the type \ccc{Traits::Less_xy_2} as specified in -the concept ConvexHullTraits\_2 and the corresponding member +the concept \ccc{ConvexHullTraits_2} and the corresponding member function that returns an instance of this type. diff --git a/Convex_hull_2/doc_tex/Convex_hull_2_ref/convex_hull_2.tex b/Convex_hull_2/doc_tex/Convex_hull_2_ref/convex_hull_2.tex index 800c9633f63..14ddfb9eaee 100644 --- a/Convex_hull_2/doc_tex/Convex_hull_2_ref/convex_hull_2.tex +++ b/Convex_hull_2/doc_tex/Convex_hull_2_ref/convex_hull_2.tex @@ -40,7 +40,7 @@ the type \ccc{InputIterator::value_type} is defined. \item \ccc{InputIterator::value_type} and \ccc{OutputIterator::value_type} are equivalent to \ccc{Traits::Point_2}. \item \ccc{Traits} contains the following subset of types from - the concept ConvexHullTraits\_2 and their corresponding member + the concept \ccc{ConvexHullTraits_2} and their corresponding member %\ccIndexMainItem[c]{ConvexHullTraits_2} functions that return instances of these types: \begin{itemize} diff --git a/Convex_hull_2/doc_tex/Convex_hull_2_ref/is_ccw_strongly_convex_2.tex b/Convex_hull_2/doc_tex/Convex_hull_2_ref/is_ccw_strongly_convex_2.tex index 4f640504413..059f5ad848e 100644 --- a/Convex_hull_2/doc_tex/Convex_hull_2_ref/is_ccw_strongly_convex_2.tex +++ b/Convex_hull_2/doc_tex/Convex_hull_2_ref/is_ccw_strongly_convex_2.tex @@ -15,7 +15,7 @@ \ccDefinition The function \ccRefName\ determines if a given sequence of points defines -a counterclockwise-oriented, stongly convex polygon. +a counterclockwise-oriented, strongly convex polygon. A set of points is said to be strongly convex if it consists of only extreme points (\textit{i.e.}, vertices of the convex hull). @@ -39,7 +39,7 @@ type \ccc{ForwardIterator::value_type} is defined. \ccHeading{Requirements} \ccc{Traits} contains the following subset of types from -the concept ConvexHullTraits\_2 and their corresponding member +the concept \ccc{ConvexHullTraits_2} and their corresponding member %\ccIndexMainItem[c]{ConvexHullTraits_2} functions that return instances of these types: \begin{itemize} diff --git a/Convex_hull_2/doc_tex/Convex_hull_2_ref/is_cw_strongly_convex_2.tex b/Convex_hull_2/doc_tex/Convex_hull_2_ref/is_cw_strongly_convex_2.tex index 7d0179256bc..de116eb3cb3 100644 --- a/Convex_hull_2/doc_tex/Convex_hull_2_ref/is_cw_strongly_convex_2.tex +++ b/Convex_hull_2/doc_tex/Convex_hull_2_ref/is_cw_strongly_convex_2.tex @@ -15,7 +15,7 @@ \ccDefinition The function \ccRefName\ determines if a given sequence of points defines -a clockwise-oriented, stongly convex polygon. +a clockwise-oriented, strongly convex polygon. A set of points is said to be strongly convex % \ccIndexMainItemDef{strongly convex} if it consists of only extreme points (\textit{i.e.}, vertices of the convex hull). @@ -40,7 +40,7 @@ type \ccc{ForwardIterator::value_type} is defined. \ccHeading{Requirements} \ccc{Traits} contains the following subset of types from -the concept ConvexHullTraits\_2 and their corresponding member +the concept \ccc{ConvexHullTraits_2} and their corresponding member %\ccIndexMainItem[c]{ConvexHullTraits_2} functions that return instances of these types: \begin{itemize} diff --git a/Convex_hull_2/doc_tex/Convex_hull_2_ref/lower_hull_points_2.tex b/Convex_hull_2/doc_tex/Convex_hull_2_ref/lower_hull_points_2.tex index 56018403ea3..269f32313bd 100644 --- a/Convex_hull_2/doc_tex/Convex_hull_2_ref/lower_hull_points_2.tex +++ b/Convex_hull_2/doc_tex/Convex_hull_2_ref/lower_hull_points_2.tex @@ -48,7 +48,7 @@ points gives the sequence of extreme points. \item \ccc{InputIterator::value_type} and \ccc{OutputIterator::value_type} are equivalent to \ccc{Traits::Point_2}. \item \ccc{Traits} contains the following subset of types from - the concept ConvexHullTraits\_2 and their corresponding member + the concept \ccc{ConvexHullTraits_2} and their corresponding member functions that return instances of these types: \begin{itemize} \item \ccc{Traits::Point_2}, diff --git a/Convex_hull_2/doc_tex/Convex_hull_2_ref/upper_hull_points_2.tex b/Convex_hull_2/doc_tex/Convex_hull_2_ref/upper_hull_points_2.tex index 3957d660aef..11b86a4e475 100644 --- a/Convex_hull_2/doc_tex/Convex_hull_2_ref/upper_hull_points_2.tex +++ b/Convex_hull_2/doc_tex/Convex_hull_2_ref/upper_hull_points_2.tex @@ -46,9 +46,9 @@ points gives the sequence of extreme points. \ccHeading{Requirements} \begin{enumerate} \item \ccc{InputIterator::value_type} and \ccc{OutputIterator::value_type} - are equilvalent to \ccc{Traits::Point_2}. + are equivalent to \ccc{Traits::Point_2}. \item \ccc{Traits} contains the following subset of types from - the concept ConvexHullTraits\_2 and their corresponding member + the concept \ccc{ConvexHullTraits_2} and their corresponding member %\ccIndexMainItem[c]{ConvexHullTraits_2} functions that return instances of these types: \begin{itemize}